Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13144 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #466 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C22×C11×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(17,22)(18,27)(19,23)(20,31)(24,39)(25,42)(26,36)(28,30)(29,37)(32,38)(33,40)(34,35)(41,45)(43,44);(12,14,15,13)(16,17,23,35,20,25,32,36,21,26,38,42,31,34,19,22)(18,24,37,46,29,39,27,40,30,41,44,47,43,45,28,33);(16,18,19,28,31,43,38,44,21,30,32,27,20,29,23,37)(17,24,22,33,34,45,42,47,26,41,36,40,25,39,35,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6132);